Anomalous Peak in the Superconducting Condensate Density of Cuprate High- $T_c$ Superconductors at a Unique Doping State

The doping dependence of the ratio of the superconducting condensate density to the effective mass, $n_s^o/m_{\mathrm{ab}}^{*}$, was studied in detail by muon-spin rotation for ${\mathrm{Y}}_{0.8}{\mathrm{Ca}}_{0.2}{\mathrm{Ba}}_2({\mathrm{Cu}}_{1-z}{\mathrm{Zn}}_z{)}_3{\mathrm{O}}_{7-\delta }$ and ${\mathrm{Tl}}_{0.5-y}{\mathrm{Pb}}_{0.5+y}{\mathrm{Sr}}_2{\mathrm{Ca}}_{1-x}{\mathrm{Y}}_x{\mathrm{Cu}}_2{\mathrm{O}}_7$. Our data show that $n_s^o/m_{\mathrm{ab}}^{*}$ exhibits a peak at a unique doping state in the overdoped regime. Its position coincides with the critical doping state, where the normal state pseudogap was reported to appear and to deplete the electronic density of states. This finding implies that the pseudogap primarily arises from a change in the electronic ground state rather than from thermal fluctuations.